W-infinity structure of the sl(N) Conformal Affine Toda theories (original) (raw)

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

1992

As recently shown the conformal affinc Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (woo algebra) is established.

A new deformation of W-infinity and applications to the two-loop WZNW and conformal affine Toda models

Physics Letters B, 1992

We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra w ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models.

Conformal affine sl2 Toda field theory

Physics Letters B, 1990

We present a model based on the ~2 affine algebra, which is integrable and conformally invariant. It reduces to the standard Liouville theory or to the sinh-Gordon model under certain limiting conditions. We find the general classical solution of this model and the exchange algebra.

Connection between the affine and conformal affine Toda models and their Hirota solution

Physics Letters B, 1993

It is shown that the Affine Toda models (AT) constitute a "gauge fixed" version of the Conformal Affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the corresponding CAT models, each one associated to a point of the orbit of the conformal group. The Hirota's τ-function are introduced and soliton solutions for the AT and CAT models associated toŜL(r + 1) and SP (r) are constructed. 1 Work partially supported by CNPq 2 supported by FAPESP

Extended C = ∞ conformal systems from classical toda field theories

Nuclear Physics B, 1989

In a recent article we showed that the bosonic Toda field theories obey extended Virasoro symmetries which involve generators of spins higher than two; and that their quantization gives a systematic treatment of generalized conformal bosonic models. Their Virasoro central charges are such that they become infinite in the classical limit. This latter situation is studied in detail in the present paper, where a simple form of the general solution of the Toda field equations is given, that allows one to separate the modes and to study the Poisson bracket structure of the generators of the extended symmetry in a systematic way. Besides its relevance to the study of integrable classical systems this paves the way to the quantum case, already discussed by the authors and to be worked out in full detail in a separate publication.

Dressing transformations and the algebraic-geometrical solutions in the conformal affine sl(2) Toda model

Physics Letters B, 1995

It is shown that the algebraic-geometrical (or quasiperiodic) solutions of the Conformal Affine sl(2) Toda model are generated from the vacuum via dressing transformations. This result generalizes the result of Babelon and Bernard which states that the N-soliton solutions are generated from the vacuum by dressing transformations. * more precisely the elements g ∓ in the affine group are fixed up to the factors exp{f ± (x ±)ĉ} where f ± are arbitrary functions

The Conserved Charges and Integrability of the Conformal Affine Toda Models

Modern Physics Letters A, 1994

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

Hirota's solitons in the affine and the conformal affine Toda models

Nuclear Physics B, 1993

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach.

Conformal Toda theory with a boundary

Journal of High Energy Physics, 2010

We investigate sℓ n conformal Toda theory with maximally symmetric boundaries. There are two types of maximally symmetric boundary conditions, due to the existence of an order two automorphism of the W n≥3 algebra. In one of the two cases, we find that there exist D-branes of all possible dimensions 0 ≤ d ≤ n − 1, which correspond to partly degenerate representations of the W n algebra. We perform classical and conformal bootstrap analyses of such D-branes, and relate these two approaches by using the semi-classical light asymptotic limit. In particular we determine the bulk one-point functions. We observe remarkably severe divergences in the annulus partition functions, and attribute their origin to the existence of infinite multiplicities in the fusion of representations of the W n≥3 algebra. We also comment on the issue of the existence of a boundary action, using the calculus of constrained functional forms, and derive the generating function of the Bäcklund transformation for sℓ 3 Toda classical mechanics, using the minisuperspace limit of the bulk one-point function.